 Checking date: 01/04/2019

Course: 2019/2020

Calculus II
(15531)
Study: Bachelor in Biomedical Engineering (257)

Coordinating teacher: ALVAREZ CAUDEVILLA, PABLO

Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS

Course:
Semester:

Branch of knowledge: Engineering and Architecture

Students are expected to have completed
Calculus I, Linear Algebra
Competences and skills that will be acquired and learning results. Further information on this link
The student will be able to formulate, solve and understand mathematically the problems arising in Biomedical Engineering. To do so it is necessary to be familiar with the n-dimensional Euclidean space, making a special emphasis in dimensions 2 and 3, visualizing the more important subsets. He/she must be able to manage (scalar and vector) functions of several variables, as well as their continuity, differentiability, and integrability properties. The student must solve optimization problems with and without restrictions and will apply the main theorems of integration of scalar and vector functions to compute, in particular, lengths, areas and volumes, moments of inertia, and heat flow.
Description of contents: programme
1. Differential Calculus in several variables 1.1. R^n as an Euclidean space; topology 1.2. Scalar and vector functions of n variables 1.3. Limits and continuity 1.4. Differentiability 2. Local properties of functions 2.1. Higher-order derivatives 2.1.1 Iterated derivatives 2.1.2. Differential operators: divergence, curl, laplacian 2.1.3. Taylor polynomial 2.2. Free and constrained optimization 2.2.1 Local extrema 2.2.2. Global extrema: free optimization problems 2.2.3. Lagrange multipliers 3. Integral Calculus in R^2 and R^3 3.1. Double and triple integrals 3.2. Changes of variables 3.3. Applications 4. Integrals over curves and surfaces 4.1. Line and path integrals 4.2. Surface integrals 4.3. Integral theorems of vector analysis
Learning activities and methodology
The learning methodology will include: - Attendance to master classes, in which core knowledge will be presented that the students must acquire. The recommended bibliography will facilitate the students' work - Resolution of exercises by the student that will serve as a self-evaluation method and to acquire the necessary skills - Exercise classes, in which problems proposed to the students are discussed - Tests - Final Exam - Tutorial sessions - The instructors may propose additional homework and activities
Assessment System
• % end-of-term-examination 60
• % of continuous assessment (assigments, laboratory, practicals...) 40
Basic Bibliography
• J. E. Marsden and A. J. Tromba. Vector Calculus, 6th. edition. W. H. Freeman. 2012
• M. D. Weir, J. Hass, and G. B. Thomas. Thomas¿ Calculus, Multivariable. Addison-Wesley. 2010